How does a neural network that has been trained keep learning while in a real world scenario
You are right. If you don't continuously train the neural network after you have deployed it, there is no way it can continuously learn or be updated with more information. You need to program the neural network to learn even after it has been deployed. There is no such thing as a neural network that decides what it does without a human deciding first what it needs to do: this is a very common misconception (probably caused by the media and science fiction movies). It's also true that you need to label your data if you intend to train the neural network in a supervised fashion, but there are other ways to train neural networks (e.g. by reinforcement learning), depending also on the problem you want to solve.
If you want to develop neural networks that can learn continually, you probably want to look into continual learning techniques for neural networks. Another term that you may be looking for is online machine learning.